HERTZIAN CONTACT STRESS CALCULATOR
When two bodies
with curved surfaces are in contact under a force, point or line
contact between these bodies changes to area contact, and 3 dimensional stresses are developed
These stresses are contact stresses. A knowledge of contact stresses is
important in calculating strength of bearings, gear and worm drives, ball
and cylindrical rollers, and cam mechanisms. Typical failures are seen as cracks, pits, or
flaking in the surface material.
The
Hertzian contact calculator is designed to calculate contact pressure and contact
stress for spherical and cylindrical contact. Maximum shear stresses are
drawn with respect to the depth from contact surface for Object1 and Object2.
The formulas used for the calculations are given in the "List of Equations"
section.
Contact representations calculated by Hertzian contact calculator are shown below. Circles represent sphere or
cylinder depending on contact selection.



SphereSphere 
SpherePlane 
SphereCup 
CylinderCylinder 
CylinderPlane 
CylinderInner Cylinder 
Calculator:
RESULTS 
Parameter 
Symbol 
Object1 
Object2 
Unit 
Maximum Hertzian contact pressure 
p_{max} 



Max shear stress 
τ_{max} 




Depth of max shear stress 
z 





Circular contact area diameter

2a



Note: Use dot "." as decimal separator.


Object1 
Object2 
Definitions:
Cylindrical contact: The contact of two cylindrical parts where the contact line turns to rectangle area
with the presence of a contact force. The area of contact is a narrow rectangle of width 2b and cylinder length l.
Modulus of elasticity (Young’s
modulus): The rate of change of unit tensile or compressive stress with respect to unit tensile or compressive strain for the condition of uniaxial
stress within the proportional limit. Typical values: Aluminum: 69 GPa, Steel: 200GPa.
Poisson’s ratio: The ratio of lateral unit strain to longitudinal unit strain under the condition
of uniform and uniaxial longitudinal stress within the proportional limit.
Proportional Limit: The largest value of stress up to which a linear relation still exist between
stress and strain (Hooke’s Law).
Spherical contact: The contact
of two spherical parts where contact point turns to a circular area of radius a
under the presence of contact force. A contact pressure pmax is occurred on this
contact area.
Shear stress: A form of a stress acts parallel to the surface (cross section) which has a cutting nature.
Stress: Average force per unit area which results strain of material.
List of Equations:
List of equations and calculation steps for Hertzian contact
stress calculations
Reference: